DES MOINES — Donald Trump holds a narrow lead over Hillary Clinton in Iowa just a handful of days before the election, according to a poll published Thursday, although Trump’s advantage does not exceed the poll’s margin for error.

If Clinton wins the national election, 1 in 5 Iowans do not think the country is ready for its first woman president.

But whomever wins the state, 3 out of 4 Iowans say they trust the election system, according to the poll.

Trump, the Republican presidential candidate, leads Clinton, the Democratic candidate, by 3 percentage points, which also is the margin for error in the Simpson College/RABA Research poll published Thursday.

“Iowa is again proving to be one of the closest states in the country,” Tim Albrecht, a RABA Research partner based in Des Moines, said in a news release accompanying the poll results. “This is a margin-of-error race, right down to the wire. We could be in for a late night on Tuesday.”

Simpson/RABA surveyed 1,076 likely Iowa voters Tuesday and Wednesday; 44 percent said they plan to vote for Trump, and 41 percent said they plan to vote for Clinton.

That 3-point lead is up slightly from Simpson/RABA’s poll from early September, when the poll showed Trump with a 1-point lead.

“Donald Trump’s base is sticking with him, even after the recent tape revealing his lewd comments about women,” said Kedron Bardwell, chair of Simpson’s political science department. “His lead with non-college voters and men surpasses Clinton’s lead with college-educated voters and women. If GOP turnout holds up, those groups will be key to the party’s chances in Iowa.”

Should Clinton win, 1 in 5 Iowa voters said — partisan feelings aside — they do not think the country is ready for a woman president. Two-thirds said they do think the country is ready for a woman president, and 14 percent said they were not sure.

At a time when Trump has raised questions about voting fraud, 3 out of 4 Iowa voters said they have confidence in the fairness and accuracy of elections conducted here. Only 12 percent said they do not have confidence in Iowa’s elections, and 14 percent said they were not sure.

The survey also revealed nearly a quarter of Iowa voters think a third political party would better represent their political views.

When given the choice between two statements, 64 percent of those surveyed said while the Democratic and Republican parties are not perfect, one represents his or her views better than a third party could.

But 23 percent said neither of the two major parties represents his or her views as well as a third party could.

That number increased among young people: 2 in 5 respondents between the ages of 18 and 29 said they think a third party could better represent their views.